Spectral analysis of natural scenes can provide much more detailed information about the scene than an ordinary RGB camera. The richer information provided by hyperspectral images has been beneficial to numerous applications, such as understanding natural environmental changes and classifying plants and soils in agriculture based on their spectral properties. In this paper, we present an efficient manifold learning based method for accurately reconstructing a hyperspectral image from a single RGB image captured by a commercial camera with known spectral response. By applying a nonlinear dimensionality reduction technique to a large set of natural spectra, we show that the spectra of natural scenes lie on an intrinsically low dimensional manifold. This allows us to map an RGB vector to its corresponding hyperspectral vector accurately via our proposed novel manifold-based reconstruction pipeline. Experiments using both synthesized RGB images using hyperspectral datasets and real world data demonstrate our method outperforms the state-of-the-art.